Optimal Execution: A Review

This review article is intended to collect and summarize many of the results in the field of optimal execution over the last twenty years. In doing so, we describe the general workings of the limit order book so that the sources of costs and risks which need to be optimized are understood. The initial models considered propose simple dynamics for prices which allow easily computable strategies which maximize risk-adjusted profits. Subsequently, the review is divided into two major parts. The first explores several works which investigate how optimal liquidation strategies are modified to account for more complex dynamics, namely other stochastic or non-linear factors. The second presents optimal trading strategies when the agent utilizes benchmarks in addition to risk-adjusted wealth, or when she has objectives beyond optimal liquidation.